[Boost-users] mcgregor_common_subgraphs usage/complexity/performance/runtime

Subject: [Boost-users] mcgregor_common_subgraphs usage/complexity/performance/runtime
From: Julian Wolf (julian.jw.wolf_at_[hidden])
Date: 2018-08-31 21:45:03

Hello everyone,

I'm new to Boost and today I tried to use the mcgregor_common_subgraphs 
functions but can't find an explanation why the function shows such bad 
performance when I use it.

According to the documentation [1] the algorithm runs in O(V1 * V2) for the 
entire space with V being the number of vertices in the two graphs. So not 
great, but I'd expect that to run in reasonable time for graphs with less than 
100 vertices.
But in my case it doesn't, therefore any help appreciated whether I have some 
error or misconception on my side or whether this is expected performance.

What I'm trying to achieve: I want to check whether two graphs have a common 
subgraph of size x. x depends on the size of smaller graph, I'm using a factor 
y for this with 0 < y < 1.

With smaller values for x (e.g. x = 0.7 * V1) the example returns very fast, 
which makes sense since a smaller part of the search space needs to be 
explored.
If I increase the factor to 0.8 * V1 or even run through the whole search 
space the program does not terminate within 10 minutes (where I canceled)

I'll attach a working example as well as two graphs (44 and 46 vertices) 
showing the behaviour described.

# gcc CommonSubgraph.cpp -o common_subgraph_example -lboost_graph -lstdc++

# time ./common_subgraph_example 0.7 graph1.dot graph2.dot
Factor 0.7
Size: 30
real    0m0.043s

# time ./common_subgraph_example 0.8 graph1.dot graph2.dot
Factor 0.8
^C
real    10m39.741s

My system runs openSUSE Tumbleweed with Boost 1.67
> rpm -q --whatprovides /usr/include/boost/graph/mcgregor_common_subgraphs.hpp
libboost_headers1_67_0-devel-1.67.0-2.3.x86_64

Thank you!
Julian

[1] https://www.boost.org/doc/libs/1_68_0/libs/graph/doc/
mcgregor_common_subgraphs.html